The 4 year old will often engage herself in adult (age not content) conversations. While it doesn't specifically bother us, we actually find it amusing, it could pose a problem when dealing with others. She is one to ask many questions and does well to comprehend the answers. For the record, we have adult content conversation in private.

If possible, we'd like for the result to be that she feel comfortable to have conversation with us, but recognize that she may not be welcome to conversations that are being held by other adults.

This is interrupting. There are lots of ways to deal with it. I liked to make physical contact - hand on arm or leg, or around waist - and eye contact and say "I'm having a conversation. You need to wait your turn unless it's an emergency." Or other times "Is it an emergency?"

But you might be asking about:

A: And then for dessert, what do you think we should serve?

B: I was thinking something chocolate, everyone likes chocolate.

B's child: Well, I don't. How about pie?

This is a tougher call. It definitely happens as children get older, and they want to join in all your conversations, whether invited or not. I would typically laugh (to indicate it's not really a big deal) and say something like "not your conversation, sweetie, go back and play" and then carry on. One of my children, by school age, needed a separate chat later about not joining adult conversations unless invited. But don't worry, as an adult that child has no reticence left about joining uninvited conversations or meeting new people :-)

When our kids interrupt a conversation, one of us squats down to eye level, places a hand on each side of the child's face, and says, "Is it urgent?" (If not) "Please let us finish and you will have my attention." Then we try to wind things up and get back down to eye level and listen to the child. The hands-on-the-face thing has become a bit of shorthand in our family for "I need your attention" and our 5-yr-old is now doing that instead of just plain ol' interrupting (at least when the adult in question is seated, or in reach; else it's a tug at the clothing or a grasping of a hand. So long as it's a non-verbal request for attention I'm good.)

We also made sure that they know that emergencies do not require them to wait, or politely request attention. (Of course, our definition of 'emergency' differs from that of a 2- or 5-yr-old...)

I encouraged this in my daughter. If the content's not inappropriate, and the kid is not interrupting about something unrelated, then why shouldn't they participate in a discussion? I found that my 4 year old had opinions pretty much as sound as other random yobbos on the issues of the day. Heck, often her more "naive" questions were the best ones to make people actually think about what they were talking about.

Personally, I detest people who don't talk to kids like they are people but instead talk to them like they're a dog or something. Their opinion on "what's for dessert" is less valid than someone else's? Why? If she's participating civilly, then I'd encourage her to talk with others in general non-private conversations. It will increase vocabulary, people, and reasoning skills (did with my daughter at least).

and what makes their opinions MORE valid than someone else's? If I'm planning the skating banquet with the other organizer, and my next door neighbour butts in to tell me what to serve for dessert, I would not consider that polite or appropriate. Not all conversations directly concern the people who can hear them. Opinions and kibbitzing are not always welcome, even when they are presented perfectly politely. I never suggested a child not get an opinion on their own dessert, simply gave a conversational fragment that might not concern one who overheard it.
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ChrysJul 31 '13 at 14:05

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@Chrys I don't read this as encouraging the child to intrude on conversations that is not relevant, but more that if you are having a conversation and the child offers a opinion treat the child as you would an adult. The nosy neighbor will be gently rebuffed, but I agree with mxyzplk that treat children as persons. I feel this is how children learns to be persons.
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IdaAug 27 '14 at 16:51

When the child want to talk to a parent who is talking, the child places his/her hand on the parent's arm. The parent then places his/her hand on the child's to let the child know that he/she has been heard.

This avoids the interruption, and validates the child's right to speak.

It is good that you are bothered by this. Too many parents say stuff which then gets repeated in playgrounds.

We just say "We're having a grown up conversation, which isn't for your ears."

In fairness, this normally makes our child retreat to a safe distance that is still within earshot, because kids are like that. Then we opt for the only real solution, which is to have the conversation when they are not around.

Now, with regards to other adults, I am not sure what you are getting at. If you are worried that she will be answering back to teachers, then that is something the teacher will soon deal with. If you are worried about friends or relatives, then they will probably find it as charming as you do. Kids ask lots of questions. Its what they do. One of the great pleasures of my life today is seeing our youngest child pester her big brother with lots of questions. Now he knows what its like!

The bottom line is this: provided you teach her good manners, such as not speaking when somebody else is speaking, and asking if its ok to interupt a conversation, then there isn't really a problem.